In parallelogram $$ABCD$$, let $$O$$ be the intersection of diagonals $$\overline{AC}$$ and $$\overline{BD}$$. Angles $$CAB$$ and $$DBC$$ are each twice as large as angle $$DBA$$, and angle $$ACB$$ is $$r$$ times as large as angle $$AOB$$. Find the greatest integer that does not exceed $$1000r$$.

(第十四届AIME1996 第15题)